Testing for unobserved heterogeneity in exponential and Weibull duration models

We examine the use of the likelihood ratio (LR) statistic to test for unobserved heterogeneity in duration models, based on mixtures of exponential or Weibull distributions. We consider both the uncensored and censored duration cases. The asymptotic null distribution of the LR test statistic is not the standard chi-square, as the standard regularity conditions do not hold. Instead, there is a nuisance parameter identified only under the alternative, and a null parameter value on the boundary of the parameter space, as in Cho and White (2007a). We accommodate these and provide methods delivering consistent asymptotic critical values. We conduct a number of Monte Carlo simulations, comparing the level and power of the LR test statistic to an information matrix (IM) test due to Chesher (1984) and Lagrange multiplier (LM) tests of Kiefer (1985) and Sharma (1987). Our simulations show that the LR test statistic generally outperforms the IM and LM tests. We also revisit the work of van den Berg and Ridder (1998) on unemployment durations and of Ghysels et al. (2004) on interarrival times between stock trades, and, as it turns out, affirm their original informal inferences.